Are Two (Samples) Really Better Than One?

Babaioff, Moshe; Gonczarowski, Yannai A.; Mansour, Yishay; Moran, Shay

doi:10.1145/3219166.3219187

Cited by 18 publications

(19 citation statements)

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“…Empirical Revenue Maximization. We follow the notation of [2] and we define the Empirical Revenue Maximization mechanism (ERM) to be the mechanism that computes the optimal price assuming that the unknown distribution F is equal to the empirical distributionF of the samples. In particular when two samples are only observed the exact form of ERM is the following…”

Section: Single Buyer -Single Item Pricingmentioning

confidence: 99%

“…One thing that we also get directly from this description is the maximum revenue and the optimal reserve price since both of them will correspond to one of the initial points on the revenue curve. The points (q i , r i ) that we start with are presented in the following table together with the value of the variables c (1) i and c (2) i that are computed according to the following equations and will be used to define the probability density function of the distribution for our counter-example.…”

Section: Lower Bound Of Approximation Ration Of Ermmentioning

confidence: 99%

“…Given that a 1 2 -factor approximation is the best that is achievable by deterministic mechanisms given one sample from a regular distribution F , can we do better given, say, two samples from the distribution? As it turns out, analyzing the revenue of mechanisms chosen using two samples from a distribution has been challenging analytically, without any progress until a very recent paper of Babaioff et al [2]. In this work, they consider the revenue of the natural Empirical Revenue Maximizing (ERM) mechanism.…”

Section: Introductionmentioning

confidence: 99%

“…Analyzing the revenue of ERM from two samples was challenging and tedious in the work of [2], and it appears difficult to improve thosee guarantees or show that they cannot be improved. Motivated by this apparent difficulty, in this paper we target developing a general framework, based on Semidefinite Programming, for analyzing the revenue attainable by mechanisms chosen using independent samples from a distribution F and evaluated on a fresh independent sample from that same distribution.…”

Section: Introductionmentioning

confidence: 99%

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More Revenue from Two Samples via Factor Revealing SDPs

Daskalakis

Zampetakis

2020

Proceedings of the 21st ACM Conference on Economics and Computation

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We consider the classical problem of selling a single item to a single bidder whose value for the item is drawn from a regular distribution F , in a "data-poor" regime where F is not known to the seller, and very few samples from F are available. Prior work [9] has shown that one sample from F can be used to attain a 1/2-factor approximation to the optimal revenue, but it has been challenging to improve this guarantee when more samples from F are provided, even when two samples from F are provided. In this case, the best approximation known to date is 0.509, achieved by the Empirical Revenue Maximizing (ERM) mechanism [2]. We improve this guarantee to 0.558, and provide a lower bound of 0.65. Our results are based on a general framework, based on factor-revealing Semidefinite Programming relaxations aiming to capture as tight as possible a superset of product measures of regular distributions, the challenge being that neither regularity constraints nor product measures are convex constraints. The framework is general and can be applied in more abstract settings to evaluate the performance of a policy chosen using independent samples from a distribution and applied on a fresh sample from that same distribution. CCS Concepts: • Theory of computation → Algorithmic game theory and mechanism design; Algorithmic mechanism design.

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Section: Single Buyer -Single Item Pricingmentioning

confidence: 99%

Section: Lower Bound Of Approximation Ration Of Ermmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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More Revenue from Two Samples via Factor Revealing SDPs

Daskalakis

Zampetakis

2020

Proceedings of the 21st ACM Conference on Economics and Computation

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“…Huang et al (2018) studies the sample complexity needed to achieve near-optimal performance. The setting where the seller has access to a limited number of observed samples (one or two samples) has also been studied; see Huang et al (2018), Fu et al (2015), Babaioff et al (2018), Allouah and Besbes (2019) and Daskalakis and Zampetakis (2020).…”

Section: Literature Reviewmentioning

confidence: 99%

Optimal Pricing with a Single Point

Allouah¹,

Bahamou²,

Besbes³

2021

Preprint

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We study the following fundamental data-driven pricing problem. How can/should a decisionmaker price its product based on observations at a single historical price? The decision-maker optimizes over (potentially randomized) pricing policies to maximize the worst-case ratio of the revenue it can garner compared to an oracle with full knowledge of the distribution of values, when the latter is only assumed to belong to broad non-parametric set. In particular, our framework applies to the widely used regular and monotone non-decreasing hazard rate (mhr) classes of distributions. For settings where the seller knows the exact probability of sale associated with one historical price or only a confidence interval for it, we fully characterize optimal performance and near-optimal pricing algorithms that adjust to the information at hand. As examples, against mhr distributions, we show that it is possible to guarantee 85% of oracle performance if one knows that half of the customers have bought at the historical price, and if only 1% of the customers bought, it still possible to guarantee 51% of oracle performance.The framework we develop leads to new insights on the value of information for pricing, as well as the value of randomization. In addition, it is general and allows to characterize optimal deterministic mechanisms and incorporate uncertainty in the probability of sale.

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Improved Two Sample Revenue Guarantees via Mixed-Integer Linear Programming

Ahunbay

Vetta

2021

Algorithmic Game Theory

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We study the performance of the Empirical Revenue Maximizing (ERM) mechanism in a single-item, single-seller, single-buyer setting. We assume the buyer's valuation is drawn from a regular distribution F and that the seller has access to two independently drawn samples from F . By solving a family of mixed-integer linear programs (MILPs), the ERM mechanism is proven to guarantee at least .5914 times the optimal revenue in expectation. Using solutions to these MILPs, we also show that the worst-case efficiency of the ERM mechanism is at most .61035 times the optimal revenue. These guarantees improve upon the best known lower and upper bounds of .558 and .642, respectively, of Daskalakis and Zampetakis [4].

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Are Two (Samples) Really Better Than One?

Cited by 18 publications

References 0 publications

More Revenue from Two Samples via Factor Revealing SDPs

More Revenue from Two Samples via Factor Revealing SDPs

Optimal Pricing with a Single Point

Improved Two Sample Revenue Guarantees via Mixed-Integer Linear Programming

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